System and methods for data compression and nonuniform quantizers

ABSTRACT

An optical network includes a transmitting portion configured to (i) encode an input digitized sequence of data samples into a quantized sequence of data samples having a first number of digits per sample, (ii) map the quantized sequence of data samples into a compressed sequence of data samples having a second number of digits per sample, the second number being lower than the first number, and (iii) modulate the compressed sequence of data samples and transmit the modulated sequence over a digital optical link. The optical network further includes a receiving portion configured to (i) receive and demodulate the modulated sequence from the digital optical link, (ii) map the demodulated sequence from the second number of digits per sample into a decompressed sequence having the first number of digits per sample, and (iii) decode the decompressed sequence.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of and priority to U.S. ProvisionalPatent Application Ser. No. 62/568,679, filed Oct. 5, 2017, and to U.S.Provisional Patent Application Ser. No. 62/573,780, filed Oct. 18, 2017,and the disclosures of both of these prior applications are incorporatedherein by reference in their entireties.

BACKGROUND

The field of the disclosure relates generally to optical communicationsystems and networks, and more particularly, to data compression,coding, and quantizers for analog and digital optical systems andnetworks.

Conventional hybrid fiber-coaxial (HFC) architectures deploy long fiberstrands from an optical hub to a fiber node, and typically many shortfiber strands to cover the shorter distances from the HFC nodes to aplurality of end users. Conventional Multiple Service Operators (MSOs)offer a variety of services, including analog/digital TV, video ondemand (VoD), telephony, and high speed data internet, over these HFCnetworks, which utilize both optical fibers and coaxial cables, andwhich provide video, voice, and data services to the end usersubscribers. The HFC network typically includes a master headend, andthe long optical fiber carries the optical signals and connects the linkbetween the headend, the hub, and the fiber node. Conventional HFCnetworks also typically include a plurality of coaxial cables to connectthe fiber nodes to the respective end users, and which also carry radiofrequency (RF) modulated analog electrical signals.

The HFC fiber node converts optical analog signals from the opticalfiber into the RF modulated electrical signals that are transported bythe coaxial cables to the end users/subscribers. Some HFC networksimplement a fiber deep architecture, and may further utilize electricalamplifiers disposed along the coaxial cables to amplify the RF analogsignals. In the conventional HFC network, both the optical andelectrical signals are in the analog form, from the hub all the way tothe end user subscriber's home. Typically, a modem termination system(MTS) is located at either the headend or the hub, and providescomplementary functionality to a modem of the respective end user.

The continuous growth of optical intra/inter-data-center link, 5G mobilefronthaul (MFH) and backhaul (MBH), next-generation distributed HFCarchitectures and access networks, passive optical networks (PONs), andhigh-speed optical short-reach transmission systems with advancedmulti-level modulation formats require an equivalent growth in thedevelopment of advanced digital multi-level modulation formats toprocess the vastly increased amount of data transmitted over the variousnetworks. Presently, conventional deployments of 1G/10G PON systemsusing nonreturn to zero (NRZ) modulation are unable to meet the growingcapacity demand to deliver future high-speed data and video services.

The growth of the optical link and network architectures has beenmatched, and in many ways outpaced, by a continuously-growing demand onhigh-speed Internet, high-definition TV, and real-time entertainmentservices, which has created an additional challenge for future broadbandaccess networks. These emerging new services, which include virtualreality and 5G, are rapidly depleting the bandwidth resources ofexisting PONs, MFH, and HFC networks, where upgrades to system capacityand spectral efficiency is urgently needed.

Some conventional communication networks operate according to DOC SIS3.1 specifications, which are standardized, and feature orthogonalfrequency-division multiplexing (OFDM) and higher order of modulations(>4096 QAM). However, although the DOCSIS specification provides higherflexibility and spectral efficiency, it also presents new technicalissues and challenges. For example, the demanding carrier-to-noise ratio(CNR) specified by DOCSIS 3.1 specifications for high order modulationscannot not be supported by legacy digital-to-analog (D/A) oranalog-to-digital (A/D) converters having resolutions and the range of8-10 digits. Replacement of every legacy D/A or A/D converter at thecustomer premises of a user would incur a substantially high cost, andtherefore there is a need in the field new algorithms that are capableof suppressing quantization noise without the McKinley impairing D/A andA/D performances. Additionally, the continuous envelope and highpeak-to-average power ratio (PAPR) of OFDM signals render the signalsvulnerable to nonlinear distortions in analog HFC networks.

Recent progress in advanced A/D and D/A quantizers and data compressiontechniques for transmitting OFDM signals is encouraging improvement tothe transmission techniques for digital RFoG (D-RFoG) systems. Somequantizer or compression techniques utilize partial bit sampling (PBS),but results in rapid increases to the quantization noise when reducingthe number of digits. Fitting based nonlinear quantization (FBNQ)operations are recommended by the standard of Open Radio EquipmentInterface (ORI). However, the FBNQ algorithm is complex and timeconsuming because it needs to estimate the statistical characteristicsfrom a large number of samples, which increases the system delay.Moreover, the accuracy of FBNQ seriously degrades when quantizing theamplitudes distributed outside the interquartile range (IQR). Somematured companding methods, including μ-law and A-law, for encodingacoustic signals have been used in tuning the quantization levels.However, the logarithmic compression function of these methods is notoptimal to suppress the quantization noise of Gaussian distributed OFDMsignals. Accordingly, new algorithms are needed for optimizing thenon-uniformly distributed quantization levels.

The growing performance requirements of 5G new-radio (NR), high-speedInternet access, and high-resolution multi-media entertainment withvirtual reality create even further challenges to future fiber-wirelessintegrated MFH. Recent 5G-NR specifications feature OFDM and higherorder modulations (e.g., 256- and 1024-QAM). However, proposals tointegrate these two technologies have resulted in new difficulties, suchas high sensitivity to nonlinear distortions and increased requirementson high-resolution D/A converters, which limit the quality andtransmission distance of analog radio-over-fiber (A-RoF) opticalnetworks in MFH. However, digital RoF (D-RoF) networks have demonstratedgreater compatibility with different formats, as well as greatersuitability for the 5G-NR environment that includes a more diversespectrum and services. D-RoF also utilizes high immunity to nonlineardistortions, and bitter capability for error-free transmissions throughuse of forward error coding/correction (FEC) techniques. Furthermore, bythe additional use of data compression and advanced modulation formats,D-RoF is better able to mitigate bandwidth and efficiency, and betterdigitally transport high-quality wireless signals between the basebandunit pool (BBU-pool) and radio access units (RAU) with increasedtransmission distance and improved power budgets. Accordingly, theresults would need to develop algorithms to improve the compressionefficiency of D-RoF MFH for 5G-NR specifications.

BRIEF SUMMARY

In an embodiment, an optical network includes a transmitting portionconfigured to (i) encode an input digitized sequence of data samplesinto a quantized sequence of data samples having a first number ofdigits per sample, (ii) map the quantized sequence of data samples intoa compressed sequence of data samples having a second number of digitsper sample, the second number being lower than the first number, and(iii) modulate the compressed sequence of data samples and transmit themodulated sequence over a digital optical link. The optical networkfurther includes a receiving portion configured to (i) receive anddemodulate the modulated sequence from the digital optical link, (ii)map the demodulated sequence from the second number of digits per sampleinto a decompressed sequence having the first number of digits persample, and (iii) decode the decompressed sequence.

In an embodiment, an analog-to-digital converter includes a samplingunit configured to sample an analog voltage signal into a sequence ofdiscrete samples, a non-uniform quantizing unit configured to quantizethe discrete digital samples with 2^(x) quantization levels, where xrepresents a first number of digits per sample. The analog-to-digitalconverter further includes a mapping unit configured to map thequantized discrete digital samples from the first number of digits persample into a second number of digits per sample, wherein the secondnumber is greater than the first number.

In an embodiment, a data compression method is provided for an inputdigital sequence of discrete signal samples having an input number ofdigits per sample. The method includes steps of applying a compandingfunction to the input signal samples according to the input number ofdigits per sample, calculating a companded output number of digits persample that is less than the input number of digits per sample,quantizing the input signal samples according to the companded outputnumber of digits per sample, and outputting a digital sequence of signalsamples having the companded output number of digits per sample.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentdisclosure will become better understood when the following detaileddescription is read with reference to the accompanying drawings in whichlike characters represent like parts throughout the drawings, wherein:

FIG. 1A is a schematic illustration of a non-uniform digital-to-analogconverter, according to an embodiment.

FIG. 1B is a schematic illustration of a non-uniform analog-to-digitalconverter, according to an embodiment.

FIG. 2 is a flow diagram for an exemplary K-law algorithm process,according to an embodiment.

FIG. 3 is a graphical illustration comparing the error-vector-magnitudeof an OFDM signal against the K-value, applying the K-law algorithmprocess depicted in FIG. 2 on the non-uniform analog-to-digitalconverter depicted in FIG. 1B.

FIG. 4A is a graphical illustration depicting an operation principle ofa relaxed Lloyd algorithm with respect to a probability densityfunction, according to an embodiment.

FIG. 4B is a graphical illustration depicting an operation principle ofa relaxed Lloyd algorithm with respect to quantization levels, accordingto an embodiment.

FIG. 5 is a flow diagram for a quantization process, according to anembodiment.

FIGS. 6A-D are graphical illustrations of the error-vector-magnitudeagainst a number of quantization digits for different algorithms,according to an embodiment.

FIG. 7 is a schematic illustration of a digital transmitter, accordingto an embodiment.

FIG. 8 is a schematic illustration of a digital receiver, according toan embodiment.

FIG. 9 is a graphical illustration of the error-vector-magnitude againsttap coefficients, according to an embodiment.

FIG. 10 is a graphical illustration depicting an operating principle ofa Lloyd algorithm on the quantization process depicted in FIG. 5.

FIG. 11 is a graphical illustration depicting the error-vector-magnitudeagainst a number of iterations and digits, according to an embodiment.

FIG. 12A is a graphical illustration depicting theerror-vector-magnitude against quantization digits with respect to aLloyd algorithm used for OFDM, according to an embodiment.

FIG. 12B is a graphical illustration depicting theerror-vector-magnitude against quantization digits with respect to aLloyd algorithm used for SC-FDM, according to an embodiment.

FIG. 13A is a schematic illustration of a D-RoF transmitter, accordingto an embodiment.

FIG. 13B is a schematic illustration of a D-RoF receiver, according toan embodiment.

FIG. 14 is a graphical illustration depictingsignal-to-quantization-noise ratio as a function of quantization digits,according to an embodiment.

FIG. 15 is a schematic illustration of a digital mobile fronthaul forcoherent transmission, according to an embodiment.

FIG. 16 is a graphical illustration depicting bit error rate versusreceived optical power, according to an embodiment.

FIG. 17 is a graphical illustration depicting the error-vector-magnitudeunder the influence of bit errors, according to an embodiment.

Unless otherwise indicated, the drawings provided herein are meant toillustrate features of embodiments of this disclosure. These featuresare believed to be applicable in a wide variety of systems including oneor more embodiments of this disclosure. As such, the drawings are notmeant to include all conventional features known by those of ordinaryskill in the art to be required for the practice of the embodimentsdisclosed herein.

DETAILED DESCRIPTION

In the following specification and the claims, reference will be made toa number of terms, which shall be defined to have the followingmeanings.

The singular forms “a,” “an,” and “the” include plural references unlessthe context clearly dictates otherwise.

“Optional” or “optionally” means that the subsequently described eventor circumstance may or may not occur, and that the description includesinstances where the event occurs and instances where it does not.

Approximating language, as used herein throughout the specification andclaims, may be applied to modify any quantitative representation thatcould permissibly vary without resulting in a change in the basicfunction to which it is related. Accordingly, a value modified by a termor terms, such as “about,” “approximately,” and “substantially,” are notto be limited to the precise value specified. In at least someinstances, the approximating language may correspond to the precision ofan instrument for measuring the value. Here and throughout thespecification and claims, range limitations may be combined and/orinterchanged; such ranges are identified and include all the sub-rangescontained therein unless context or language indicates otherwise.

As used herein, the terms “processor” and “computer” and related terms,e.g., “processing device”, “computing device”, and “controller” are notlimited to just those integrated circuits referred to in the art as acomputer, but broadly refers to a microcontroller, a microcomputer, aprogrammable logic controller (PLC), an application specific integratedcircuit (ASIC), and other programmable circuits, and these terms areused interchangeably herein. In the embodiments described herein, memorymay include, but is not limited to, a computer-readable medium, such asa random access memory (RAM), and a computer-readable non-volatilemedium, such as flash memory. Alternatively, a floppy disk, a compactdisc-read only memory (CD-ROM), a magneto-optical disk (MOD), and/or adigital versatile disc (DVD) may also be used. Also, in the embodimentsdescribed herein, additional input channels may be, but are not limitedto, computer peripherals associated with an operator interface such as amouse and a keyboard. Alternatively, other computer peripherals may alsobe used that may include, for example, but not be limited to, a scanner.Furthermore, in the exemplary embodiment, additional output channels mayinclude, but not be limited to, an operator interface monitor.

Further, as used herein, the terms “software” and “firmware” areinterchangeable, and include any computer program storage in memory forexecution by personal computers, workstations, clients, and servers.

As used herein, the term “non-transitory computer-readable media” isintended to be representative of any tangible computer-based deviceimplemented in any method or technology for short-term and long-termstorage of information, such as, computer-readable instructions, datastructures, program modules and sub-modules, or other data in anydevice. Therefore, the methods described herein may be encoded asexecutable instructions embodied in a tangible, non-transitory, computerreadable medium, including, without limitation, a storage device and amemory device. Such instructions, when executed by a processor, causethe processor to perform at least a portion of the methods describedherein. Moreover, as used herein, the term “non-transitorycomputer-readable media” includes all tangible, computer-readable media,including, without limitation, non-transitory computer storage devices,including, without limitation, volatile and nonvolatile media, andremovable and non-removable media such as a firmware, physical andvirtual storage, CD-ROMs, DVDs, and any other digital source such as anetwork or the Internet, as well as yet to be developed digital means,with the sole exception being a transitory, propagating signal.

Furthermore, as used herein, the term “real-time” refers to at least oneof the time of occurrence of the associated events, the time ofmeasurement and collection of predetermined data, the time for acomputing device (e.g., a processor) to process the data, and the timeof a system response to the events and the environment. In theembodiments described herein, these activities and events occursubstantially instantaneously.

According to the embodiments described herein, digitization transmissionscheme may advantageously transmit digitized radio signals through theoptical fiber link and convert the signal back into analog format atremote fiber nodes. This digitized radio transmission scheme is furtheruseful for utilization in MFH networks using a common public radiointerface (CPRI). The transmission scheme implements a sufficient numberof quantization digits and FEC, such that digitized radio carriers maybe reconstructed by a D/A converter with no quality degradation.Additionally, the digital compression algorithm techniques describedherein enable further reduction of the number of digits, and with asuppressed quantization noise floor. According to these advantageoussystems and methods, the transmission efficiency (TE, defined as theratio between the effective bandwidths of the encapsulated analogsignals and the converted digital signals) of the network issubstantially improved.

Non-Uniform Quantizers for Analog and Digital Systems

The following embodiments describe algorithms for optimizingnon-uniformly distributed quantization levels, and to resolve thechallenges arising from use of PBS, FBNQ, and the logarithmiccompression function of companding levels. A first such algorithm isbased on the K-parameter fast statistical estimation (FSE), alsoreferred to as K-law. This algorithm embodiment proves to becomputationally efficient, and particularly useful for OFDM signals withGaussian distributed amplitudes. A second algorithm is based on therelaxed Lloyd algorithm (R-Lloyd), and is useful for determining thedecision threshold and quantization levels based on minimum square errorcriteria. This R-Lloyd-based technique (i) is compatible with multipleformats, (ii) is not limited to Gaussian distributions, and (iii)exhibits lower quantization noise level with fewer digits (sometimesthough, at the expense of increased computing complexity).

FIG. 1A is a schematic illustration of a non-uniform D/A converter 100.FIG. 1B is a schematic illustration of a non-uniform A/D converter 102.Converters 100, 102 may be implemented as one or more discrete hardwarecomponents, as a system of individual software modules, or as acombination thereof. In an exemplary embodiment, D/A converter 100includes and input signal 104, or x_(F)(k). Input signal 104 may, forexample, represent a digital signal sampled at 15 digits per sample.Input signal 104 is fed into a map 106. In the example illustrated inFIG. 1, map 106 is a 15-to-8-bit map, which then outputs 8 digits persample to a non-uniform inverse quantizer 108. That is, the data sampleswith 15-digits per sample are mapped to 8-digits per sample. Inversequantizer 108 converts the 8-digit samples into voltage levels and sendsthe inverse-quantized signal to an interpolator 110, which determinesthe amplitude of the voltage pulses input from inverse quantizer 108,and then outputs an analog voltage 112, or x_(A)(k). In someembodiments, the 15-to-8-digits mapping of map 106 may be determinedaccording to the present K-law algorithm techniques, and a bits-to-levellook-up table that may be used by inverse quantizer 108 may bedetermined according to the present R-Lloyd algorithm techniques.

The respective processing modules of non-uniform A/D converter 102 aresubstantially similar to those of non-uniform D/A converter 100, butfunction substantially in reverse. That is, an input analog voltage 114,or x_(A)(k), is sampled by a sampler 116 (i.e., instead of aninterpolator). At a non-uniform quantizer 118, the sampled signal isquantized with 2⁸ quantization levels and output as 8-digits-per-samplechips. The 8-digits-per-sample chips are received at map 120, where theyare mapped to 15-digits chips and output as an output signal 122, orx_(r)(k). Similar to D/A converter 100, quantizer 118 and 8-to-15-digitslook-up-tables may be determined or controlled by the present K-law orR-Lloyd algorithm techniques.

FIG. 2 is a flow diagram for an exemplary K-law algorithm process 200.In an exemplary embodiment, process 200 utilizes the present K-lawalgorithm to generate the 15-to-8-digits look-up table of map 106, FIG.1A, and the 8-to-15-digits look-up table for map 120, FIG. 1B, as wellas non-uniform quantizers 108, 118, respectively.

Process 200 begins at step 202, in which the 15 digit samples are inputto D/A converter 100, FIG. 1. In an alternative embodiment of step 202,process 200 operates in reverse, and is applied to the input signal ofA/D converter 102. In step 204, the input samples are subject to atraining companding function, C(x), which, in K-law, may be representedaccording to:

$\begin{matrix}{{{C(x)} = {\frac{1}{\Delta}{{erf}\left( \frac{Kx}{\sqrt{2}} \right)}}},\; {x \in \left\lbrack {0,1} \right\rbrack}} & \left( {{Eq}.\mspace{11mu} 1} \right)\end{matrix}$

where Δ=1−2 Φ(−K), Φ is the cumulative distribution function (CDF) ofthe standard Gaussian distribution, and x is the normalized modulus ofthe input signal. In K-law, K is the key parameter to be configured, andthe modulus of the OFDM signal is assumed to be distributed on [0+Kσ],where σ is the standard deviation.

In step 206, the normalized modulus x of the input signal is swept from1-2¹⁵ times. In step 208, the companded output y=C(x) is calculated. Instep 210, the output y is subject to 8-bit quantization. In step 212,process 200 implements the 8-to-15-bit lookup table (or the 15-to-8-bitlookup table for the other converter). The practical value of theK-values calculated according to process 200 are described further belowwith respect to FIG. 3.

FIG. 3 is a graphical illustration 300 comparing theerror-vector-magnitude (EVM) 302 of an OFDM signal against the K-value304, applying K-law algorithm process 200, FIG. 2, on non-uniform A/Dconverter 102, FIG. 1B. In an exemplary embodiment, illustration 300shows the EVM performance of a one-frame LTE-like OFDM signal carriermodulated by QPSK, 16 QAM, or 64 QAM with 286720 samples. From theexperimental results shown in illustration 300, it can be seen that anoptimal point 306 on distribution curves 308 occurs at a K value ofabout 2.7.

These K-law techniques enable fast statistical estimation. Nevertheless,a more accurate technique for selecting quantization levels uses a Lloydalgorithm, and further based on minimum mean-square error criterion(MMSE). Prior to performance of the Lloyd algorithm, the probabilitydensity function (PDF) of the signal amplitudes is divided into multiplesegments and the borders of each segment are given by the thresholds[t_(i) t_(t+1)]. After quantization, the amplitude falls within eachsegment is quantized as level l_(i). The MMSE between the quantized andoriginal signals, {t_(i)} and {l_(i)}, may then be minimized accordingto the following equations:

$\begin{matrix}{{l_{i} = \frac{\int_{t_{i - 1}}^{t_{i}}{{{xf}(x)}{dx}}}{\int_{t_{i - 1}}^{t_{i}}{{f(x)}{dx}}}},} & \left( {{Eq}.\mspace{11mu} 2} \right) \\{{and}\text{:}} & \; \\{{t_{i} = \frac{l_{i} + l_{i + 1}}{2}},} & \left( {{Eq}.\mspace{11mu} 3} \right)\end{matrix}$

where f(x) is the PDF of signal modulus.

FIG. 4A is a graphical illustration depicting an operation principle 400of the relaxed Lloyd algorithm with respect to PDF 402. Principle 400thus demonstrates the effect of decision thresholds t_(i) andquantization levels l_(i) on PDF 402 of x. FIG. 4B is a graphicalillustration depicting an operation principle 404 of the relaxed Lloydalgorithm with respect to quantization levels 406. Principle 404 thusdemonstrates the effect of interpolation of minor quantization levels406. A flow diagram of a quantization process using the relaxed Lloydalgorithm is described further below with respect to FIG. 5.

FIG. 5 is a flow diagram for a quantization process 500. In an exemplaryembodiment, quantization process 500 is implemented by, within, or inassociation with, one or both of quantizers 108, FIG. 1A, and 118, FIG.1B. Process 500 begins at step 502, in which process 500 estimates f(x),with x=|s|. In step 504, the quantization thresholds are initiated as(t₁, t₂, . . . t_(N+1))|=0, or (t_(1,0), t_(2,0), . . . t_(N+1,0)),where N=2^(p) and p presents the number of major digits. In an exemplaryembodiment of step 504, selection of the initial quantization thresholdsuses boundaries of uniformly distributed segments. In step 506, thequantization levels (l_(1,1), l_(2,1), . . . l_(N,1)) are calculatedusing (t_(1,0), t_(2,0), . . . t_(N+1,0)) based on Eq. 2.

In step 508, the quantization thresholds (t_(1,1), t_(2,1), . . .t_(N+1,1)) are similarly obtained, using (l_(1,1), 1 _(2,1), . . .l_(N,1)), and according to Eq. 3. Step 510 is a decision step. In step510, process 500 determines whether the value for j is less than apredetermined value M of the iteration index. If, in step 510, j<M,process 500 returns to step 506. In this manner, process 500 is able toprocess a repeatable loop such that the quantization thresholds andquantization levels are repeatedly updated, based on the former value oftheir counterpart, until the iteration index reaches M (i.e., j=M), uponwhich process 500 proceeds to step 512. In step 512, process 500 isconfigured to interpolate minor quantization levels (k_(K(1)), l_(K(2)),. . . l_(K (q))) such that the minor quantization levels are uniformlyinserted between l_(K) and l_(K+1), where q represents the number ofminor digits. Process 500 and completes after step 512.

In an exemplary embodiment of process 500, the selection of p and q maybe optimized according to a trade-off between the quantization accuracyand computational complexity. Typically, a large p value leads toimproved precision at the expense of increased number of iterations tobe converged. In contrast, if the value for p is too large, strongquantization noise may result within small-probability-density regionsdue to the number of training samples falling into that region beinginsufficient, thus reducing the confidence level of the estimation.Considering all of these factors, given a total number of digits of D,the value for p may be set at 5, and the value for q may be determinedaccording to q=(D−5). A comparison of preliminary results between thedifferent algorithms is described further below with respect to FIG. 6.

FIGS. 6A-D graphical illustrations 600 of EVM against a number ofquantization digits for different algorithms 602. More particularly,FIG. 6A illustrates a comparative plot 604 of EVM versus quantizationdigits using pulse coding modulation (PCM) for the several differentalgorithms 602. FIG. 6B illustrates a close-up view of a portion ofcomparative plot 604. FIG. 6C illustrates a comparative plot 606 of EVMversus quantization digits using differential PCM (DPCM) for the severaldifferent algorithms 602. FIG. 6D illustrates a close-up view of aportion of comparative plot 606. As can be seen from comparative plots604 and 606, optimal EVM performance is obtained using the presentR-Lloyd non-uniform quantizer algorithm, and particularly in the casewhere 3-6 quantization digits are applied.

As described above, the non-uniform quantizer embodiments describedherein are capable of reducing the number of sampling digits, and alsoof suppressing the quantization noise levels. As described furtherbelow, the present non-uniform quantizer is also particularly usefulwith respect to D-RoF and D-RFoG systems. As described above, D-RoFinterfaces have been used in MFH systems, such as CPRI and the open basestation architecture initiative (OBSAI), which converts the analog radiosignals into digital format and delivers digitized baseband radiocarriers from a radio equipment controller (REC) to radio equipment(RE). According to the embodiments described above, using a sufficientnumber of quantization digits and FEC, the digitized radio carriers maybe advantageously reconstructed by a D/A converter with no qualitydegradation.

The present embodiments are still further useful for achievingsignificant benefits, in comparison with conventional techniques, over aD-RFoG link between a hub and distributed remote fiber nodes. Thepresent techniques are format-agnostic, with simple hardwareimplementation, at the distributed remote fiber nodes. The presenttechniques are still further capable of taking advantage of thedigitization benefits of the link, including the high immunity tononlinear distortions from power amplification. Essentially error-freetransmission may therefore be achieved through use of FEC, enabled bythe high capacity from the fiber network. In combination with thenon-uniform quantizer the systems and methods described herein, therequired number digits and quantization noise floor for converting eachanalog sample may be further reduced, thereby significantly increasingthe capacity of the D-RFoG systems in comparison with conventionaltechniques.

FIG. 7 is a schematic illustration of a digital transmitter 700. In anexemplary embodiment, transmitter 700 is configured for operation withina D-RFoG system/network, and is capable of executing DPCM, as well asthe K-law aunt/or R-Lloyd based non-uniform quantizers and algorithmsdescribed above. More particularly, transmitter 700 may include one ormore of an analog signal input 702, a high-resolution A/D converter 704,a DPCM encoder 706, a bit map 708, and a modulator 710 in operablecommunication with a channel 712. In exemplary operation of transmitter700, implementation of DPCM with at least one of the present non-uniformquantizers will significantly minimize the quantization noise. In thisrespect, DPCM encoder 706 is configured to include one or more of acompression unit 714, a quantizer 716, and expander unit 718, and afeedback circuit 720. Feedback circuit 720 may further include a filter722, which may be a one-tap finite impulse response (FIR) filter havinga response function defined by C(z)=/βz⁻¹, where the β is the tapcoefficient, and may have a large impact on the quantizationperformance.

FIG. 8 is a schematic illustration of a digital receiver 800. Similar tothe embodiments described above, receiver 800 is similar to transmitter700, FIG. 7, in its structural architecture, but essentially operatingin reverse order. More particularly, receiver 800 may include one ormore of a channel input 802, a demodulator 804, a bit map 806, a DPCMdecoder 808, and a D/A converter 810 configured to output an analogsignal 812. In exemplary operation, DPCM decoder 808 is configured tohave a feedback circuit 814 that corresponds to feedback circuit 722 oftransmitter 700.

FIG. 9 is a graphical illustration 900 of EVM against tap coefficients.In an exemplary embodiment, graphical illustration 900 depicts the EVMof analog signals 812 from receiver 800, FIG. 8, versus the tapcoefficient β. As can be seen from graphical illustration 900, for aone-frame OFDM signal having 20×7 symbols, 2048 total subcarriers, and1201 loaded subcarriers, optimal performance is achieved for values ofβ≈0.6.

Data-Compression for Digital Mobile Fronthaul with Algorithm andDifferential Coding

The differential-coded Lloyd algorithms described above are alsoparticularly useful as a data-compression technology for improvingbandwidth efficiencies in digital MFH networks. The followingembodiments demonstrate proof of concept with respect to experimentalresults demonstrating milestone transmissions of 180 Gbps over 80-kmfronthaul links, and encapsulating 64×100-MHz 1024-QAM 5G-NR carrierswith lower-than-0.5% EVM.

FIG. 10 is a graphical illustration depicting an operating principle1000 of a Lloyd algorithm on quantization process 500, FIG. 5. In anexemplary embodiment, operating principle 1000 leverages the operationalresults shown in FIG. 4A for a digital RoF or MFH system. In exemplaryoperation of operating principle 1000, samples 1002 are taken of ananalog wireless OFDM waveform 1004 to form a discrete signal. Thediscrete signal is then quantized into U levels and converted into abinary A×C chip 1006 having U digits 1008. The value for U may beobtained, for example, according to the CPRI standard setting U=15. EachA×C chip 1006 is then subject to compression, and mapped from U digits1008 to V digits 1010.

In the exemplary embodiment, V<U, and the bandwidth efficiency maytherefore be improved according to the relationship (U−V)/V×100%. Asdescribed above, the Lloyd algorithm is based on MMSE criterion, anddivides the PDF of the signal amplitudes into multiple segments withboundaries defined by the thresholds [t_(i) t_(i+1)] as shown in FIG.4A. After quantization, the amplitudes falling into each segment maythen be quantized as level l_(i). To minimize MSE between the quantizedand original signals, {t_(i), t_(i+1)} and l_(i) may be related throughimplementation of Eq. 2 and Eq. 3, where f(x) represents the PDF ofsignal amplitudes. The flow diagram of this relaxed Lloyd algorithm isdescribed above with respect to FIG. 5, i.e., process 500, which followssubstantially the same order as described above. Using this process,both quantization levels and thresholds gradually converge to thepositions resulting in the minimum MSE between original and quantizedsignals.

In the case of a compressed A×C chip 1006 having V digits 1010, anR-Lloyd method may be further implemented to reduce the complexity ofthe conventional Lloyd algorithm, where 2^(P) out of 2^(V) levels arecomputed using the conventional Lloyd algorithm first as the majorlevels and 2^((V-P)) minor quantization levels are uniformlyinterpolated between [l_(i) l_(i+1)]. The selection of P and V maytherefore be determined by a trade-off between the quantization accuracyand convergence speed, similar to the embodiments described above.

FIG. 11 is a graphical illustration 1100 depicting EVM against a numberof iterations and digits. More particularly, illustration 1100 depicts afirst EVM curve 1102 against iterations for six major digits and twominor digits. Similarly, a second EVM curve 1104 is depicted for fivemajor digits and three minor digits, a third EVM curve 1106 is depictedfor four major digits and four minor digits, and a fourth EVM curve isdepicted for three major digits and five minor digits. Therefore, fromillustration 1100, the convergence speed of the OFDM EVM may be observedfor the application of different numbers of major digits (e.g., under15-to-8-digits compression, or U=15 and V=8). As demonstrated inillustration 1100, with fewer major digits, faster convergence speed maybe achieved with fewer iterations. According to EVM curve 1106, in thecase where 4 major digits (P=4) are applied, the converged EVM value canbe obtained with approximately 100 iterations. In the particularexamples illustrated in FIG. 11, and optimal balance between complexityand accuracy is reached using 4 and 5 major digits.

FIG. 12A is a graphical illustration 1200 depicting EVM againstquantization digits with respect to a Lloyd algorithm 1202, incomparison with other algorithms 1204, used for OFDM. FIG. 12B is agraphical illustration 1206 depicting EVM against quantization digitswith respect to Lloyd algorithm 1202 and other algorithms 1204 used forsingle carrier frequency division multiplexing (SC-FDM). Moreparticularly, illustrations 1200, 1206, depicted the EVM performance ofOFDM and SC-FDM radio signals, respectively, after 15-to-8-digitcompression and de-compression.

From illustrations 1200, 1206, it can be seen that, in comparison otheralgorithms 1204 (e.g., μ-Law, A-Law, FSE, etc.), R-Lloyd algorithm 1202is capable of realizing the most optimal EVM performance, and usingfewer quantization digits. Additionally, although some algorithmicmethods (e.g., FSE) are specially designed for OFDM signals havingGaussian distributed amplitudes these and other algorithms are notapplicable to non-Gaussian signals, such as SC-FDM. According to thepresent embodiments though, performance of the present Lloyd algorithmtechniques is independent of the statistical property of the givensignal. That is, the same algorithmic techniques may be applied toGaussian and non-Gaussian signals, as demonstrated by illustration 1206.As shown in FIG. 12B, acceptable EVM values may still the obtained whenusing Lloyd algorithm to compress SC-FDM radio signals. In the examplesdepicted in FIGS. 12A-B, the required EVM thresholds of 64-, 256-,1024-, and 4096-QAM are set at 8%, 3.5%, 1.68%, and 0.7%, respectively.

The present systems and methods are additionally capable ofadvantageously applying DPCM techniques to further improve the signalquality after compression. In comparison with conventional PCM, whichdigitizes the original radio signal x(k), DPCM may be additionallyutilized to predict and digitize the differential signal, namely,x(k)−x(k−1). For DPCM, most source signals exhibit some correlationsbetween successive samples. Through differential precoding, thecorrelation-induced redundancy may be reduced to enable representationof the information with fewer digits. To reduce the correspondingcomplexity, a first-order differentiator may be used, and havingpre-coded signals, which are denoted here as d(k)=x(k)−βx(k−1).

Under simulated test conditions, the value of β was found to beoptimized at the value of 0.6. Nevertheless, DPCM implementations mayexhibit specific challenges with respect to the quantization errorresulting from the compression process, and the decision error exhibitedat the DPCM decoder. Those two types of errors propagated andaccumulated from the beginning to the end of the whole frame, which mayseriously degrade the quality of the reconstructed analog RF signals.The embodiments described further below resolve these challenges byproviding a feedback loop-based differential quantizer that mitigatesthe quantization error transfer issue.

FIG. 13A is a schematic illustration of a D-RoF transmitter 1300. FIG.13B is a schematic illustration of a D-RoF receiver 1302. In theexemplary embodiment, transmitter 1300 and receiver 1302 are implementedwith respect to a 5G MFH system. Transmitter 1300 may include one ormore of 5G-NR analog carriers 1304 being input to a high-resolution A/Dconverter 1306, a DPCM encoder 1308, a bit map 1310, and a modulator1312 that outputs a signal to MFH network 1314. In an exemplaryembodiment, transmitter 1300 further includes a compression unit 1316 inoperable communication with one or both of D PCM encoder 1308 and bitmap 1310. In at least one embodiment, transmitter 1300 may substitute aPCM encoder for DPCM encoder 1308.

In a similar manner, receiver 1302 provides a signal from MFH network1314 to a demodulator 1316, and may further include one or more of a bitmap 1318, a DPCM decoder (or PCM decoder) 1320, and a D/A converter 1322configured to output 5G-NR analog carriers 1324 to one or both of anenhanced mobile broadband (eMBB) network 1326 and a massive MIMO network1328. In this example, receiver 1302 further includes a de-compressionunit 1330 in operable communication with one or both of bit map at 1318and DPCM decoder 1320.

Under test conditions, a simple IM/DD link tests the performance of thecompressed D-RoF link of transmitter 1300 and receiver 1302. Attransmitter 1300, for example, one 20-MHz LTE OFDM component is sampledwith a resolution of 15-digits/sample, and at a sampling rate of30.72-MHz. DPCM (or PCM) encoder 1308, integrated with a Lloyd-basedaccording to the present embodiments, converts the quantized samplesinto binary A×C chips. Bit map 1310 (e.g., a 15-to-8-bit map) thencompresses each A×C chip from 15-bits/chip to 8-bits/chip. Thecompressed A×C chips may then be interleaved and mapped into NRZsymbols.

At receiver 1302, a similar process, but in reverse, may be implementedto reconstruct the analog components by decompressing the receiveddigital signals. The recovered analog component carriers (e.g., analogcarriers 1324) may then be sent to wireless antennas in RAUs in networks1326, 1328. The EVM performances of recovered analog signals 1324 maythen be compared between DPCM and PCM encoded schemes, according to oneor more of the techniques described above.

FIG. 14 is a graphical illustration 1400 depictingsignal-to-quantization-noise ratio (SQNR) as a function of quantizationdigits. In the exemplary embodiment depicted in FIG. 14, several plots1402 of SQNR versus quantization digits are illustrated with respect toa first set of compression techniques 1404 applied to a PCM codingscheme, and a second set of compression techniques 1406 applied to aDPCM coding scheme. From illustration 1400, it may be observed thatimplementation of a DPCM coding scheme instead of a PCM coding schemewill result in approximately a 1.4 dB improvement in SQNR, that is,according to the estimate SQNR≈1/EVM². Furthermore, in comparison withPBS techniques with low-order digits directly removed, the combinationof the present DPCM coding scheme and Lloyd algorithm results inapproximately a 6.2-dB gain in SQNR.

FIG. 15 is a schematic illustration of a digital MFH 1500 for coherenttransmission. In an exemplary embodiment, MFH 1500 represents a 5G-NRcompatible, high-capacity, digital MFH link. MFH 1500 includes atransmitting portion 1502 and a receiving portion 1504, which areconfigured to communicate over a transport medium 1506 (e.g., an opticalfiber, a standard single mode fiber (SSMF), etc.). In operation of MFH1500, 5G-NR-like OFDM symbols 1508 are digitized and encapsulated intoA×C chips 1510, which are interleaved and packetized why a quantizationand data compression module 1512, into D-RoF frames 1514.

Frames 1514 fed into a dual-polarization IQ modulator (DP-IQM) 1516,which modulates four streams 1518 of D-RoF signals for I and Qtributaries on both polarizations (e.g., x and y) based on, for example,QPSK modulation formats. Transmitting portion 1502 then transmits thesignals to a coherent receiver 1520 of receiving portion 1504 overmedium 1506 (e.g., an 80-km SSMF), and then sampled by, for example, a4-channel real-time sampling oscilloscope 1522 before application ofdigital signal processing (e.g., off-line) by a coherent digital signalprocessor 1524 for signal de-compression by a de-compression unit 1526and recovery. In this exemplary embodiment, the testing operation wasaccomplished using DP-QPSK with 128- and 180-Gbps data rates applied,which enabled encapsulation of 48 and 64, respectively, 100-MHz5G-NR-like OFDM components with 1024-QAM.

FIG. 16 is a graphical illustration 1600 depicting BER versus receivedoptical power. In the exemplary embodiment illustrated in FIG. 16, BERperformance plots 1602 using DP-QPSK, at different Gbaud rates, aredepicted for selected constellations 1604 of recovered OFDM signals. Inthis example, the recovered OFDM signals have 0.46% EVM under error-freecoherent transmission. The results of illustration 1600 are consideredfurther below with respect to FIG. 17.

FIG. 17 is a graphical illustration 1700 depicting EVM under theinfluence of bit errors. In the exemplary embodiment illustrated in FIG.17, illustration 1700 depicts EVM performance plots 1702 of recoveredwireless signals under the influence of bit errors (e.g., using abalanced photodetector). That is, under test conditions, the quality ofthe recovered OFDM signal it is observed while the OFDM signal is underthe influence of bit errors. From illustrations 1600 and 1700, it may beseen that, due to the error transfer challenge presented by differentialdecoding, DPCM coding schemes are more sensitive to bit errors than PCMcoding schemes. Nevertheless, this difference may be mitigated by theappropriate application of Reed-Solomon FEC (e.g., RS-FEC 528/514)according to the CPRI specification.

The present systems and methods provide an innovative combination ofenhanced data-compression algorithms, which may be based on both a Lloydalgorithm and DPCM, to improve the SQNR and bandwidth efficiency in atleast D-RoF systems for next-generation 5G-NR-compatible digital MFH, aswell as the other types of communication networks described herein. With8-digit quantization, the present D-RoF link the embodiments are capableof supporting up to at least 4096-QAM OFDM or SC-FDM formats, with up toat least 6-dB SQNR improvement. Furthermore, the present embodimentshave demonstrated how 128- and 180-Gbps high-capacity MFH links based oncoherent transmission technology may more efficiently transmit 48×100and 64×100-Mhz 5G-NR-like OFDM components with high-order 1024-QAMformat.

Exemplary embodiments of systems and methods for non-uniform quantizersand data compression are described above in detail. The systems andmethods of this disclosure though, are not limited to only the specificembodiments described herein, but rather, the components and/or steps oftheir implementation may be utilized independently and separately fromother components and/or steps described herein.

Although specific features of various embodiments of the disclosure maybe shown in some drawings and not in others, this is for convenienceonly. In accordance with the principles of the disclosure, a particularfeature shown in a drawing may be referenced and/or claimed incombination with features of the other drawings.

Some embodiments involve the use of one or more electronic or computingdevices. Such devices typically include a processor or controller, suchas a general purpose central processing unit (CPU), a graphicsprocessing unit (GPU), a microcontroller, a reduced instruction setcomputer (RISC) processor, an application specific integrated circuit(ASIC), a programmable logic circuit (PLC), a field programmable gatearray (FPGA), a DSP device, and/or any other circuit or processorcapable of executing the functions described herein. The processesdescribed herein may be encoded as executable instructions embodied in acomputer readable medium, including, without limitation, a storagedevice and/or a memory device. Such instructions, when executed by aprocessor, cause the processor to perform at least a portion of themethods described herein. The above examples are exemplary only, andthus are not intended to limit in any way the definition and/or meaningof the term “processor.”

This written description uses examples to disclose the embodiments,including the best mode, and also to enable any person skilled in theart to practice the embodiments, including making and using any devicesor systems and performing any incorporated methods. The patentable scopeof the disclosure is defined by the claims, and may include otherexamples that occur to those skilled in the art. Such other examples areintended to be within the scope of the claims if they have structuralelements that do not differ from the literal language of the claims, orif they include equivalent structural elements with insubstantialdifferences from the literal language of the claims.

What is claimed is:
 1. An optical network, comprising: a transmittingportion configured to (i) encode an input digitized sequence of datasamples into a quantized sequence of data samples having a first numberof digits per sample, (ii) map the quantized sequence of data samplesinto a compressed sequence of data samples having a second number ofdigits per sample, the second number being lower than the first number,and (iii) modulate the compressed sequence of data samples and transmitthe modulated sequence over a digital optical link; a receiving portionconfigured to (i) receive and demodulate the modulated sequence from thedigital optical link, (ii) map the demodulated sequence from the secondnumber of digits per sample into a decompressed sequence having thefirst number of digits per sample, and (iii) decode the decompressedsequence.
 2. The network of claim 1, wherein the transmitting portioncomprises an analog-to-digital converter configured to digitize ananalog signal into the input digitized stream of symbols.
 3. The networkof claim 1, wherein the transmitting portion comprises a bit map moduleconfigured to map the quantized sequence of data samples into thecompressed sequence of data samples.
 4. The network of claim 1, whereinthe transmitting portion comprises an encoder configured to performquantization on the input digitized sequence of data samples.
 5. Thenetwork of claim 4, wherein the encoder as further configured to performquantization using a relaxed Lloyd algorithm.
 6. The network of claim 5,wherein the relaxed Lloyd algorithm is based on a minimum mean-squareerror criterion.
 7. The network of claim 5, wherein the relaxed Lloydalgorithm is differential-coded.
 8. The network of claim 7, wherein theencoder is further configured to implement differential pulse codemodulation.
 9. The network of claim 8, wherein the encoder comprises aquantizer and a transmitter feedback circuit.
 10. The network of claim9, wherein the transmitter feedback circuit comprises a transmitterfinite impulse response (FIR) filter.
 11. The network of claim 10,wherein the receiving portion comprises a decoder having a receiver FIRfilter configured to correspond with the impulse response of thetransmitter FIR filter.
 12. The network of claim 11, wherein the impulseresponse comprises a response function C(z) according to:C(z)=βz ⁻¹, where β represents a tap coefficient.
 13. The network ofclaim 9, wherein the transmitter feedback circuit further comprises atleast one of a compression module and an expander module.
 14. Thenetwork of claim 5, wherein the encoder is further configured toimplement pulse code modulation.
 15. The network of claim 1, wherein thefirst number is 15 and the second number is
 8. 16. An analog-to-digitalconverter, comprising: a sampling unit configured to sample an analogvoltage signal into a sequence of discrete samples; a non-uniformquantizing unit configured to quantize the discrete digital samples with2^(x) quantization levels, where x represents a first number of digitsper sample; and a mapping unit configured to map the quantized discretedigital samples from the first number of digits per sample into a secondnumber of digits per sample, wherein the second number is greater thanthe first number.
 17. A data compression method for an input digitalsequence of discrete signal samples having an input number of digits persample, the method comprising the steps of: applying a compandingfunction to the input signal samples according to the input number ofdigits per sample; calculating a companded output number of digits persample that is less than the input number of digits per sample;quantizing the input signal samples according to the companded outputnumber of digits per sample; and outputting a digital sequence of signalsamples having the companded output number of digits per sample.
 18. Themethod of claim 17, further comprising a step looking up the inputnumber of digits per sample and the output number of digits per samplefrom a table.
 19. The method of claim 17, wherein the step of quantizingimplements a relaxed Lloyd algorithm.
 20. The method of claim 17,wherein the step of quantizing implements a K-law algorithm.